# Numeration and Counting

Math > Math Concepts  > Numeration

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## Numeration

 1.  Understanding numbers is  fundamental  and the basis for all of Mathematics. 2.  Every student at every level of education must have a firm understanding of    number.       Various systems of writing numbers can be and should be addressed at later stages of the student's development, but these systems are best understood once the base 10 system is firmly understood.     Why base 10?  well, we have 10 fingers; fundamentally, counting is done with our fingers at the earliest level.  So, it is normal to count using our fingers using one after the other like this:  1, 2, 3, 4, 5, 6, 7, 8, 9, 10.  Now, we've run out of fingers, I suppose we could then use our toes, but then at 20 we'd run out both fingers and toes... time to bring your friends into the picture!  No, it's probably best to group by tens and write down a mark for  each '10' we pass by; then when we're done counting the number of 10s we have is the number of marks we wrote down and the excess would be the number of fingers we used past the last 10.  Now using both we'd have the number of objects we were counting.      (Zero, '0', is problematic; without resorting to algebra theory, explaining zero can be a challenge;  If you start with 5 pencils in a pencil box then you could count them one at a time and finally say there are '5' pencils in the box.  This will make sense.  Then after giving all 5 pencils away, the box will become empty.  At this point there are no pencils in the box and we assign the number zero to represent the absence of pencils.    In actuality zero is a placeholder in the decimal numbering system and it is this direction that should be taken with the concept of the number zero.)     Numbers as quantity; approach numbers this way at first.  Cardinality refers to quantity, we are therefore talking about cardinal numbers (ordinal numbers will have to wait!)     Numbers mean, then, "how many."  And this is the approach to take no matter the student's grade level and ability.   Use a hands on approach counting similar objects, always count similar objects (doing so reinforces later algebra concepts.)   Count books, count pencils, count pens, count marbles, count dolls, count pennies, count quarters, count dollars, count whatever, but do not count "things."  Again, this is to reinforce algebra skills later on.       Move the objects from a larger pile to smaller piles in groups of ten, starting with one when counting.  1,2,3,4,5,6,7,8,9,10... one group, then start on the next group 11,12,13,14,15,16,17,18,19,20 ... group 2, etc.  Making smaller groups has the added benefit of not losing track of where you were counting if you get interrupted, i.e., count the groups 10, 20, 30, etc, then move into the partial, remaining group  and continue 61, 62, 63, 64 , for example.    After counting becomes routine, interrupt the counting at various times to reinforce the benefit of making groups while counting.
 This is another FREE Decimals PRINTABLE presented to you from the Numeration section of K12math.com